Problem: All of the 3rd grade teachers and students from Covington went on a field trip to an archaeology museum. Tickets were $$6.50$ each for teachers and $$2.50$ each for students, and the group paid $$48.50$ in total. A few weeks later, the same group visited a science museum where the tickets cost $$26.00$ each for teachers and $$11.00$ each for students, and the group paid $$203.00$ in total. Find the number of teachers and students on the field trips.
Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${6.5x+2.5y = 48.5}$ ${26x+11y = 203}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-4$ ${-26x-10y = -194}$ ${26x+11y = 203}$ Add the top and bottom equations together. ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $ {6.5x+2.5y = 48.5}$ to find $x$ ${6.5x + 2.5}{(9)}{= 48.5}$ $6.5x+22.5 = 48.5$ $6.5x = 26$ $x = \dfrac{26}{6.5}$ ${x = 4}$ You can also plug ${y = 9}$ into $ {26x+11y = 203}$ and get the same answer for $x$ ${26x + 11}{(9)}{= 203}$ ${x = 4}$ There were $4$ teachers and $9$ students on the field trips.